Finite Group Databasebeta

← D11×#3503 #15662096

Subgroups — D11×#3503 #15662096

Order 2816.

7478 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082435C211yesmaximal, characteristic, complemented
2#13082434C212yesmaximal, complemented
3#13082433C212yesmaximal, complemented
4#13082432C213yesmaximal, complemented
5#13082431C216yesmaximal, complemented
6#13082430C216yesmaximal, complemented
7#13082429C212yesmaximal, complemented
8#13082428C213yesmaximal, complemented
9#13082427C216yesmaximal, complemented
10Q82×D11C212yesmaximal, complemented
11D11×#557C212yesmaximal, complemented
12D11×#554C216yesmaximal, complemented
13D4×Q8×D11C216yesmaximal, complemented
14D11×#544C216yesmaximal, complemented
15D11×#533C213yesmaximal, complemented
16C2×D11×C4⋊Q8C213yesmaximal, complemented
17D11×#520C212yesmaximal
18C4×#41×D11C211yesmaximal, characteristic
19C11×#3503C211yesmaximal, characteristic, complemented
20C2×#41×D11C2211yescharacteristic
21C22×Q8×D11C2216yes—
22Q82×C11C2212yescomplemented
23C11×#557C2212yescomplemented
24C11×#554C2216yescomplemented
25D4×Q8×C11C2216yescomplemented
26C11×#544C2216yescomplemented
27C11×#533C2213yescomplemented
28C2×C11×C4⋊Q8C2213yescomplemented
29C11×#520C2212yes—
30C4×C11×#41C2211yescharacteristic
31#10623358C2212yes—
32#41×Dic11C2211yescharacteristic
33Q8×C22⋊D11C22112yescomplemented
34C2×#66997C2216yescomplemented
35#10623261C2216yescomplemented
36#10623260C22112yescomplemented
37#10623260C22112yescomplemented
38#10623259C2213yescomplemented
39#10623259C2213yescomplemented
40#10623258C22112yescomplemented
41#10623258C2216yescomplemented
42D11×C4⋊Q8C2216yes—
43D11×C4⋊Q8C2213yes—
44D11×C4⋊Q8C2216yes—
45D11×C4⋊Q8C2216yes—
46D11×C4⋊Q8C2211yescharacteristic
47D11×C4⋊Q8C22112yes—
48D11×C4⋊Q8C2216yescomplemented
49D11×C4⋊Q8C2216yescomplemented
50D11×C4⋊Q8C2216yescomplemented
51D11×C4⋊Q8C2216yescomplemented
52#10623253C22112yescomplemented
53#10623253C2216yescomplemented
54#10623252C2216yescomplemented
55#10623221C22112yescomplemented
56#10623220C22112yescomplemented
57#10623220C22112yescomplemented
58#10623219C2216yescomplemented
59D11×#125C22112yes—
60D11×#125C2216yes—
61#10623216C22112yescomplemented
62#10623167C22124yescomplemented
63#10623166C22112yescomplemented
64#10623163C22112yescomplemented
65#10623163C22124yescomplemented
66D11×C22⋊Q8C2216yes—
67D11×C22⋊Q8C22124yes—
68D11×C22⋊Q8C2216yes—
69#10623154C22124yescomplemented
70#10623153C2216yescomplemented
71#10623153C2216yescomplemented
72#10623110C2216yescomplemented
73#10623109C2216yescomplemented
74#10623109C2216yescomplemented
75Q8×D44C2216yescomplemented
76#10623105C2214yes—
77C4×#4343C2211yescharacteristic
78C4×#4343C2211yescharacteristic
79C4×Q8×D11C2216yes—
80C4×Q8×D11C2216yes—
81C4×Q8×D11C2211yescharacteristic
82C4×Q8×D11C2214yes—
83C4×Q8×D11C2211yescharacteristic
84#10623101C2212yescomplemented
85#10623100C2214yescomplemented
86#10623098C2216yescomplemented
87Q8×Dic22C2216yescomplemented
88Q8×Dic22C2214yescomplemented
89Q8×Dic22C2212yescomplemented
90#10623077C22112yes—
91C4×D4×D11C2213yes—
92C4×D4×D11C22112yes—
93C4×D4×D11C2213yes—
94#10623074C2216yescomplemented
95#10623070C22112yescomplemented
96D4×Dic22C2216yescomplemented
97D4×Dic22C22112yescomplemented
98C4×#4341C2213yes—
99C4×#4341C2213yes—
100#10623054C2216yes—
101#10623053C2213yes—
102D11×#117C2216yes—
103D11×#117C2213yes—
104#10623050C2216yescomplemented
105#10623050C2216yescomplemented
106#10623048C2216yescomplemented
107#10623042C22112yescomplemented
108#10623035C2216yes—
109C2×C4⋊C4×D11C2216yes—
110C2×C4⋊C4×D11C2216yes—
111#10623031C2216yescomplemented
112C2×#66941C2216yescomplemented
113C2×#66941C2216yescomplemented
114C4×#4339C2213yes—
115C2×C42×D11C2213yes—
116#10623001C2213yescomplemented
117C2×#66922C2213yescomplemented
118C2×C11×#41C2311yescharacteristic
119C22×Q8×C11C2316yes—
120#41×D11Q8116yescomplemented
121C2×#4343C2311yescharacteristic
122C2×Q8×D11—424no—
123C2×Q8×D11C2316yes—
124C2×Q8×D11C2312yes—
125C2×Q8×D11C23112yes—
126C2×Q8×D11C23112yes—
127C2×Q8×D11C23112yes—
128C2×Q8×D11C2311yescharacteristic
129C2×#4341C2313yes—
130C2×D4×D11C2313yes—
131C2×#4339C2313yes—
132C22×C4×D11C2313yes—
133C22×C4×D11C2313yes—
134C22×C4×D11C23112yes—
135C22×C4×D11C2313yes—
136C22×Dic22C2316yes—
137C22×Dic22C23112yes—
138C11×C4⋊Q8C2316yes—
139C11×C4⋊Q8C2316yes—
140C11×C4⋊Q8C23112yes—
141C11×C4⋊Q8C2313yes—
142C11×C4⋊Q8C2316yes—
143C11×C4⋊Q8C2311yescharacteristic
144C11×#125C2316yes—
145C11×#125C23112yes—
146C11×C22⋊Q8C2316yes—
147C11×C22⋊Q8C2316yes—
148C11×C22⋊Q8C23124yes—
149C4×Q8×C11C2311yescharacteristic
150C4×Q8×C11C2314yes—
151C4×Q8×C11C2316yes—
152C4×Q8×C11C2316yes—
153C4×Q8×C11C2311yescharacteristic
154C4×D4×C11C2313yes—
155C4×D4×C11C2313yes—
156C4×D4×C11C23112yes—
157C11×#117C2316yes—
158C11×#117C2313yes—
159C2×C11×C4⋊C4C2316yes—
160C2×C11×C4⋊C4C2316yes—
161C2×C42×C11C2313yes—
162#66999C2316yes—
163#66999C23124yes—
164#66999C2316yes—
165Q8×Dic11C2316yes—
166Q8×Dic11C2316yes—
167Q8×Dic11C2311yescharacteristic
168Q8×Dic11C2314yes—
169Q8×Dic11C2311yescharacteristic
170#66997C23112yes—
171#66997C23112yes—
172#66997C23124yes—
173#66997C2316yes—
174#66997C23112yes—
175#66997C2312yes—
176D4×Dic11C2313yes—
177D4×Dic11C2313yes—
178D4×Dic11C23112yes—
179C4×C22⋊D11C2316yes—
180C4×C22⋊D11C2316yes—
181C4×C22⋊D11C23124yes—
182#66979C2316yes—
183#66979C2313yes—
184C2×C4⋊Dic11C2316yes—
185C2×C4⋊Dic11C2316yes—
186#66977C2316yes—
187#66977C2316yes—
188#66977C23124yes—
189C2×Dic11⋊C4C23112yes—
190C2×Dic11⋊C4C23112yes—
191C2×C4×Dic11C2313yes—
192C2×C4×Dic11C2313yes—
193C2×C4×Dic11C2313yes—
194#66950C2316yes—
195#66950C2316yes—
196#66950C23124yes—
197#66949C23112yes—
198#66949C23124yes—
199#66949C23124yes—
200#66949C23112yes—
201#66946C2313yes—
202#66946C23112yes—
203#66946C2313yes—
204#66945C2316yes—
205#66945C2316yes—
206#66945C2313yes—
207#66945C2313yes—
208C4⋊C4×D11C2313yes—
209C4⋊C4×D11C2316yes—
210C4⋊C4×D11C2316yes—
211C4⋊C4×D11C23112yes—
212C4⋊C4×D11C23112yes—
213C4⋊C4×D11C23112yes—
214C4⋊C4×D11C2312yes—
215C4⋊C4×D11C2312yes—
216C4⋊C4×D11C23112yes—
217C4⋊C4×D11C23112yes—
218C4⋊C4×D11C23112yes—
219C4⋊C4×D11C23112yes—
220C4⋊C4×D11C2313yes—
221C4⋊C4×D11C23112yes—
222#66943C23112yes—
223#66943C2316yes—
224#66943C2316yes—
225#66943C23112yes—
226#66942C23124yes—
227#66942C23112yes—
228#66942C23124yes—
229#66942C23112yes—
230#66941C23112yes—
231#66941C23112yes—
232#66941C23112yes—
233#66941C23112yes—
234#66941C23124yes—
235#66941C2316yes—
236#66941C2316yes—
237#66941C23112yes—
238#66941C23112yes—
239#66941C23112yes—
240#66941C23112yes—
241#66941C2312yes—
242#66941C2312yes—
243#66940C23112yes—
244#66940C2313yes—
245#66940C2316yes—
246#66940C23112yes—
247#66940C2316yes—
248#66940C2313yes—
249#66940C23112yes—
250(C22⋊D11)⋊C4C2316yes—
251(C22⋊D11)⋊C4C2316yes—
252(C22⋊D11)⋊C4C23124yes—
253C22⋊C4×D11C23112yes—
254C22⋊C4×D11C2316yes—
255#66931C23112yes—
256#66931C23112yes—
257#66931C23124yes—
258#66931C23124yes—
259#66930C2316yes—
260#66930C23112yes—
261C4×D44C2313yes—
262C4×D44C23112yes—
263C4×D44C2313yes—
264#66925C2316yes—
265#66925C23112yes—
266C42×D11C2311yescharacteristic
267C42×D11C2313yes—
268C42×D11C2313yes—
269C42×D11C2313yes—
270C42×D11C23112yes—
271C42×D11C2313yes—
272C42×D11C2313yes—
273C42×D11C2313yes—
274C42×D11C2313yes—
275#66923C2316yes—
276#66923C23112yes—
277#66922C2313yes—
278#66922C2316yes—
279#66922C2316yes—
280#66922C2316yes—
281#66922C2311yescharacteristic
282#66922C23112yes—
283C4×Dic22C2313yes—
284C4×Dic22C2316yes—
285C4×Dic22C2313yes—
286C4×Dic22C2316yes—
287C4×Dic22C23112yes—
288C4×Dic22C23112yes—
289C4×Dic22C23112yes—
290C2×#3503—111nomaximal, Sylow
291C23×D11C2413yes—
292C11×#41C2×Q818yescomplemented
293C2×Q8×C11—412no—
294C2×Q8×C11C2416yes—
295C2×Q8×C11C2412yes—
296C2×Q8×C11C24112yes—
297C2×Q8×C11C2411yescharacteristic
298C2×D4×C11C2413yes—
299C22×C4×C11C2413yes—
300C22×C4×C11C2413yes—
301C22×C4×C11C24112yes—
302C22×C4×C11C2413yes—
303C2×C22⋊D11C2416yes—
304C22×Dic11C2413yes—
305C22×Dic11C2413yes—
306C22×Dic11C24112yes—
307C22×Dic11C2413yes—
308#4343C2×Q818yescomplemented
309Q8×D11—224no—
310Q8×D11—28no—
311Q8×D11—424no—
312Q8×D11—424no—
313Q8×D11—424no—
314Q8×D11C2×Q818yescomplemented
315#4341C2×Q8124yescomplemented
316D4×D11C2×Q8124yescomplemented
317#4339C2×Q8124yescomplemented
318C2×D44C2413yes—
319C2×C4×D11—212no—
320C2×C4×D11—212no—
321C2×C4×D11—424no—
322C2×C4×D11C2×Q8124yescomplemented
323C2×C4×D11C2414yes—
324C2×C4×D11C2413yes—
325C2×C4×D11C2413yes—
326C2×C4×D11C2413yes—
327C2×C4×D11C2413yes—
328C2×C4×D11C2413yes—
329C2×C4×D11C2413yes—
330C2×C4×D11C24112yes—
331C2×C4×D11C24124yes—
332C2×C4×D11C2413yes—
333C2×C4×D11C2411yescharacteristic
334C2×C4×D11C2413yes—
335C2×C4×D11C2413yes—
336C2×C4×D11C2411yescharacteristic
337C2×C4×D11C2411yescharacteristic
338C2×Dic22—412no—
339C2×Dic22—424no—
340C2×Dic22C2412yes—
341C2×Dic22C2414yes—
342C2×Dic22C2416yes—
343C2×Dic22C24112yes—
344C2×Dic22C24112yes—
345C2×Dic22C24124yes—
346C2×Dic22C2413yes—
347C11×C4⋊C4C2412yes—
348C11×C4⋊C4C2413yes—
349C11×C4⋊C4C24112yes—
350C11×C4⋊C4C2416yes—
351C11×C4⋊C4C24112yes—
352C11×C4⋊C4C24112yes—
353C11×C4⋊C4C2413yes—
354C11×C4⋊C4C2416yes—
355C11×C4⋊C4C24112yes—
356C11×C4⋊C4C2412yes—
357C11×C22⋊C4C24112yes—
358C11×C22⋊C4C2416yes—
359C42×C11C2413yes—
360C42×C11C2413yes—
361C42×C11C24112yes—
362C42×C11C2411yescharacteristic
363C42×C11C2413yes—
364C22⋊Dic11C24112yes—
365C22⋊Dic11C2416yes—
366(C2×D11)⋊C4C24112yes—
367(C2×D11)⋊C4C2416yes—
368(C2×D11)⋊C4C2416yes—
369(C2×D11)⋊C4C24112yes—
370C4⋊Dic11C2412yes—
371C4⋊Dic11C2413yes—
372C4⋊Dic11C24112yes—
373C4⋊Dic11C2416yes—
374C4⋊Dic11C24112yes—
375C4⋊Dic11C2413yes—
376C4⋊Dic11C24112yes—
377C4⋊Dic11C2416yes—
378C4⋊Dic11C24112yes—
379C4⋊Dic11C2412yes—
380Dic11⋊C4C2414yes—
381Dic11⋊C4C24112yes—
382Dic11⋊C4C24112yes—
383Dic11⋊C4C24112yes—
384Dic11⋊C4C2416yes—
385Dic11⋊C4C2416yes—
386Dic11⋊C4C24112yes—
387Dic11⋊C4C24112yes—
388Dic11⋊C4C24124yes—
389Dic11⋊C4C24124yes—
390Dic11⋊C4C2414yes—
391Dic11⋊C4C24112yes—
392C4×Dic11C2413yes—
393C4×Dic11C2413yes—
394C4×Dic11C24112yes—
395C4×Dic11C2413yes—
396C4×Dic11C2413yes—
397C4×Dic11C24112yes—
398C4×Dic11C2411yescharacteristic
399C4×Dic11C2411yescharacteristic
400C4×Dic11C2411yescharacteristic
401C4×Dic11C2413yes—
402C4×Dic11C2413yes—
403C4×Dic11C2413yes—
404C4×Dic11C2413yes—
405C4×Dic11C2413yes—
406C4×Dic11C24112yes—
407#3503—112no—
408#3503—112no—
409#3503—116no—
410#3503—116no—
411#3503—116no—
412#3503—113no—
413#3503—113no—
414#3503—112no—
415#3503—111no—
416#3503D1111yescharacteristic, direct product factor
417C2×Q82—112no—
418C2×#557—112no—
419C2×#554—116no—
420C2×D4×Q8—116no—
421C2×#544—116no—
422C2×#533—113no—
423C22×C4⋊Q8—113no—
424C2×#520—112no—
425C2×C4×#41—111no—
426C23×C11C2513yes—
427C22×D11—26no—
428C22×D11—26no—
429C22×D11C22×Q8112yes—
430C22×D11C2513yes—
431C22×D11C2511yescharacteristic
432Q8×C11—212no—
433Q8×C11—24no—
434Q8×C11—412no—
435Q8×C11C22×Q814yescomplemented
436D4×C11C22×Q8112yescomplemented
437C2×C4×C11—26no—
438C2×C4×C11—26no—
439C2×C4×C11—412no—
440C2×C4×C11C22×Q8112yescomplemented
441C2×C4×C11C2514yes—
442C2×C4×C11C2513yes—
443C2×C4×C11C2513yes—
444C2×C4×C11C25112yes—
445C2×C4×C11C2513yes—
446C2×C4×C11C2511yescharacteristic
447C2×C4×C11C2511yescharacteristic
448C2×C4×C11C2511yescharacteristic
449C22⋊D11C22×Q8124yescomplemented
450C2×Dic11—26no—
451C2×Dic11—26no—
452C2×Dic11—412no—
453C2×Dic11C22×Q8112yescomplemented
454C2×Dic11C2514yes—
455C2×Dic11C2513yes—
456C2×Dic11C2513yes—
457C2×Dic11C25112yes—
458C2×Dic11C2513yes—
459C2×Dic11C2511yescharacteristic
460C2×Dic11C2511yescharacteristic
461C2×Dic11C2511yescharacteristic
462D44C22×Q8112yescomplemented
463C4×D11—26no—
464C4×D11—224no—
465C4×D11—26no—
466C4×D11—28no—
467C4×D11—26no—
468C4×D11—26no—
469C4×D11—26no—
470C4×D11—26no—
471C4×D11—424no—
472C4×D11C22×Q814yes—
473C4×D11C22×Q8112yes—
474C4×D11C22×Q8112yescomplemented
475C4×D11C22×Q8112yescomplemented
476C4×D11H(5,𝔽2)14yes—
477C4×D112−1+414yes—
478Dic22—212no—
479Dic22—24no—
480Dic22—224no—
481Dic22—28no—
482Dic22—412no—
483Dic22—424no—
484Dic22C22×Q8112yescomplemented
485C22×#41—111no—
486C23×Q8—116no—
487Q82—1112no—
488Q82—116no—
489Q82—114no—
490Q82—112no—
491Q82—116no—
492Q82C2×D1112yescomplemented
493#557—116no—
494#557—1112no—
495#557—116no—
496#557—114no—
497#557—112no—
498#557C2×D1112yescomplemented
499#554—116no—
500#554—1112no—
501#554—1112no—
502#554—1124no—
503#554—116no—
504#554—1112no—
505#554—116no—
506#554—1112no—
507#554C2×D1116yescomplemented
508D4×Q8—1112no—
509D4×Q8—1112no—
510D4×Q8—116no—
511D4×Q8—1112no—
512D4×Q8—1124no—
513D4×Q8—116no—
514D4×Q8—1112no—
515D4×Q8—116no—
516D4×Q8C2×D1116yescomplemented
517#544—1112no—
518#544—1112no—
519#544—1112no—
520#544—1112no—
521#544—1124no—
522#544—116no—
523#544—116no—
524#544—116no—
525#544C2×D1116yescomplemented
526#533—113no—
527#533—113no—
528#533—116no—
529#533—116no—
530#533—116no—
531#533—116no—
532#533—116no—
533#533—116no—
534#533—113no—
535#533C2×D1113yescomplemented
536C2×C4⋊Q8—116no—
537C2×C4⋊Q8—113no—
538C2×C4⋊Q8—116no—
539C2×C4⋊Q8—116no—
540C2×C4⋊Q8—116no—
541C2×C4⋊Q8—111no—
542C2×C4⋊Q8—1112no—
543C2×C4⋊Q8—116no—
544C2×C4⋊Q8—116no—
545C2×C4⋊Q8—116no—
546C2×C4⋊Q8—116no—
547C2×C4⋊Q8—116no—
548C2×C4⋊Q8—116no—
549C2×C4⋊Q8—113no—
550C2×C4⋊Q8C2×D1113yescomplemented
551C2×#125—116no—
552C2×#125—1112no—
553C2×C22⋊Q8—116no—
554C2×C22⋊Q8—116no—
555C2×C22⋊Q8—1124no—
556#520—112no—
557#520—114no—
558#520—1112no—
559#520—116no—
560#520—116no—
561#520C2×D1112yes—
562C4×#41—111no—
563C4×#41—111no—
564C4×#41—111no—
565C4×#41—113no—
566C4×#41—113no—
567C4×#41—113no—
568C4×#41—113no—
569C4×#41C2×D1111yescharacteristic
570C2×C4×Q8—111no—
571C2×C4×Q8—111no—
572C2×C4×Q8—114no—
573C2×C4×Q8—116no—
574C2×C4×Q8—116no—
575C2×C4×D4—113no—
576C2×C4×D4—113no—
577C2×C4×D4—1112no—
578C2×#117—113no—
579C2×#117—116no—
580C22×C4⋊C4—116no—
581C22×C4⋊C4—116no—
582C22×C42—113no—
583C22×C11—23no—
584C22×C11—23no—
585C22×C11C23×Q816yes—
586C22×C11C2611yescharacteristic
587C2×D11—23no—
588C2×D11—23no—
589C2×D11—224no—
590C2×D11C23×Q816yes—
591C2×D11C23×Q812yes—
592C2×D11C2×H(5,𝔽2)12yes—
593C2×D11C2×2−1+412yes—
594C4×C11—23no—
595C4×C11—212no—
596C4×C11—23no—
597C4×C11—24no—
598C4×C11C23×Q812yes—
599C4×C11C23×Q816yes—
600C4×C11C2×H(5,𝔽2)12yes—
601C4×C11C2×2−1+412yes—
602Dic11—212no—
603Dic11—23no—
604Dic11—24no—
605Dic11—23no—
606Dic11C23×Q816yes—
607Dic11C23×Q812yes—
608Dic11C2×H(5,𝔽2)12yes—
609Dic11C2×2−1+412yes—
610C2×#41—1116no—
611C2×#41—111no—
612C2×#41—113no—
613C2×#41—113no—
614C2×#41C22×D1111yescharacteristic
615C22×Q8—111no—
616C22×Q8—112no—
617C22×Q8—116no—
618C22×Q8—1112no—
619C22×Q8—1112no—
620C22×Q8—1112no—
621C22×Q8—1112no—
622C22×Q8—116no—
623C22×Q8—4424no—
624C22×Q8C22×D1116yes—
625C22×D4—113no—
626C23×C4—113no—
627C23×C4—113no—
628C23×C4—113no—
629C23×C4—1112no—
630C4⋊Q8—116no—
631C4⋊Q8—1112no—
632C4⋊Q8—1112no—
633C4⋊Q8—1112no—
634C4⋊Q8—112no—
635C4⋊Q8—1124no—
636C4⋊Q8—116no—
637C4⋊Q8—116no—
638C4⋊Q8—1112no—
639C4⋊Q8—1112no—
640C4⋊Q8—1112no—
641C4⋊Q8—1112no—
642C4⋊Q8—1112no—
643C4⋊Q8—1112no—
644C4⋊Q8—112no—
645C4⋊Q8—112no—
646C4⋊Q8—1124no—
647C4⋊Q8—1112no—
648C4⋊Q8—1112no—
649C4⋊Q8—113no—
650C4⋊Q8—116no—
651C4⋊Q8—116no—
652C4⋊Q8—116no—
653C4⋊Q8—111no—
654C4⋊Q8—1112no—
655C4⋊Q8C22×D1113yes—
656C4⋊Q8C22×D1116yes—
657C4⋊Q8C22×D1116yes—
658C4⋊Q8C22×D1116yes—
659C4⋊Q8C22×D1111yescharacteristic
660C4⋊Q8C22×D11112yes—
661#125—1112no—
662#125—1112no—
663#125—116no—
664#125—116no—
665#125—1124no—
666#125—1124no—
667#125—1112no—
668#125—1112no—
669#125—116no—
670#125—1112no—
671#125C22×D1116yes—
672#125C22×D11112yes—
673C22⋊Q8—116no—
674C22⋊Q8—116no—
675C22⋊Q8—1124no—
676C22⋊Q8—116no—
677C22⋊Q8—116no—
678C22⋊Q8—1124no—
679C22⋊Q8—1112no—
680C22⋊Q8—116no—
681C22⋊Q8—1112no—
682C22⋊Q8—116no—
683C22⋊Q8—1124no—
684C22⋊Q8—1124no—
685C22⋊Q8—1124no—
686C22⋊Q8—1112no—
687C22⋊Q8—1112no—
688C22⋊Q8—1124no—
689C22⋊Q8—1124no—
690C22⋊Q8C22×D1116yes—
691C22⋊Q8C22×D1116yes—
692C22⋊Q8C22×D11124yes—
693C4×Q8—111no—
694C4×Q8—111no—
695C4×Q8—114no—
696C4×Q8—116no—
697C4×Q8—116no—
698C4×Q8—113no—
699C4×Q8—113no—
700C4×Q8—1112no—
701C4×Q8—1112no—
702C4×Q8—116no—
703C4×Q8—1112no—
704C4×Q8—116no—
705C4×Q8—113no—
706C4×Q8—113no—
707C4×Q8—1112no—
708C4×Q8—1112no—
709C4×Q8—116no—
710C4×Q8—1112no—
711C4×Q8—116no—
712C4×Q8C22×D1111yescharacteristic
713C4×Q8C22×D1111yescharacteristic
714C4×Q8C22×D1114yes—
715C4×Q8C22×D1116yes—
716C4×Q8C22×D1116yes—
717C4×D4—113no—
718C4×D4—113no—
719C4×D4—1112no—
720C4×D4—116no—
721C4×D4—116no—
722C4×D4—1124no—
723C4×D4—113no—
724C4×D4—113no—
725C4×D4—1112no—
726C4×D4—116no—
727C4×D4—116no—
728C4×D4—1124no—
729C4×D4—113no—
730C4×D4—113no—
731C4×D4—1112no—
732C4×D4C22×D1113yes—
733C4×D4C22×D1113yes—
734C4×D4C22×D11112yes—
735#117—113no—
736#117—116no—
737#117—113no—
738#117—113no—
739#117—116no—
740#117—116no—
741#117—116no—
742#117—1112no—
743#117—116no—
744#117—1112no—
745#117C22×D1113yes—
746#117C22×D1116yes—
747C2×C4⋊C4—1112no—
748C2×C4⋊C4—116no—
749C2×C4⋊C4—1112no—
750C2×C4⋊C4—116no—
751C2×C4⋊C4—116no—
752C2×C4⋊C4—116no—
753C2×C4⋊C4—1112no—
754C2×C4⋊C4—1112no—
755C2×C4⋊C4—1112no—
756C2×C4⋊C4—1112no—
757C2×C4⋊C4—1112no—
758C2×C4⋊C4—1112no—
759C2×C4⋊C4—112no—
760C2×C4⋊C4—113no—
761C2×C4⋊C4—113no—
762C2×C4⋊C4—112no—
763C2×C4⋊C4—1112no—
764C2×C4⋊C4—1112no—
765C2×C4⋊C4C22×D1116yes—
766C2×C4⋊C4C22×D1116yes—
767C2×C22⋊C4—1112no—
768C2×C22⋊C4—116no—
769C2×C42—113no—
770C2×C42—113no—
771C2×C42—113no—
772C2×C42—113no—
773C2×C42—1112no—
774C2×C42—113no—
775C2×C42—113no—
776C2×C42—113no—
777C2×C42—113no—
778C2×C42—113no—
779C2×C42—113no—
780C2×C42—111no—
781C2×C42C22×D1113yes—
782C2×C11—26no—
783C2×C11C24×Q811yescharacteristic
784C2×C11C22×H(5,𝔽2)11yescharacteristic
785C2×C11C22×2−1+411yescharacteristic
786D11—26no—
787D11#350314yesdirect product factor
788C24—113no—
789#41—118no—
790#41—1124no—
791#41—1124no—
792#41Q8×D1118yescomplemented
793C2×Q8—412no—
794C2×Q8—118no—
795C2×Q8—113no—
796C2×Q8—114no—
797C2×Q8—112no—
798C2×Q8—1112no—
799C2×Q8—116no—
800C2×Q8—1124no—
801C2×Q8—1112no—
802C2×Q8—2224no—
803C2×Q8—228no—
804C2×Q8—4412no—
805C2×Q8—4424no—
806C2×Q8—4424no—
807C2×Q8—4424no—
808C2×Q8—4424no—
809C2×Q8C23×D1112yes—
810C2×Q8C23×D1116yes—
811C2×Q8C23×D11112yes—
812C2×Q8C23×D1111yescharacteristic
813C2×D4—116no—
814C2×D4—1124no—
815C2×D4—113no—
816C2×D4C23×D1113yes—
817C22×C4—113no—
818C22×C4—1124no—
819C22×C4—113no—
820C22×C4—111no—
821C22×C4—111no—
822C22×C4—111no—
823C22×C4—113no—
824C22×C4—113no—
825C22×C4—113no—
826C22×C4—113no—
827C22×C4—1112no—
828C22×C4—114no—
829C22×C4—113no—
830C22×C4—113no—
831C22×C4—113no—
832C22×C4—113no—
833C22×C4—113no—
834C22×C4—113no—
835C22×C4—1112no—
836C22×C4—1124no—
837C22×C4—2212no—
838C22×C4—2212no—
839C22×C4—4424no—
840C22×C4C23×D1113yes—
841C22×C4C23×D1113yes—
842C22×C4C23×D11112yes—
843C22×C4C23×D1113yes—
844C4⋊C4—1112no—
845C4⋊C4—116no—
846C4⋊C4—1112no—
847C4⋊C4—116no—
848C4⋊C4—1124no—
849C4⋊C4—1112no—
850C4⋊C4—1124no—
851C4⋊C4—1112no—
852C4⋊C4—114no—
853C4⋊C4—112no—
854C4⋊C4—116no—
855C4⋊C4—113no—
856C4⋊C4—116no—
857C4⋊C4—113no—
858C4⋊C4—114no—
859C4⋊C4—112no—
860C4⋊C4—1112no—
861C4⋊C4—1112no—
862C4⋊C4—1112no—
863C4⋊C4—1112no—
864C4⋊C4—1112no—
865C4⋊C4—1112no—
866C4⋊C4C23×D1116yes—
867C4⋊C4C23×D1116yes—
868C4⋊C4C23×D11112yes—
869C4⋊C4C23×D11112yes—
870C4⋊C4C23×D1112yes—
871C4⋊C4C23×D1113yes—
872C4⋊C4C23×D1113yes—
873C4⋊C4C23×D1112yes—
874C4⋊C4C23×D11112yes—
875C4⋊C4C23×D11112yes—
876C22⋊C4—1112no—
877C22⋊C4—116no—
878C22⋊C4—1112no—
879C22⋊C4—116no—
880C22⋊C4—116no—
881C22⋊C4—1112no—
882C22⋊C4C23×D11112yes—
883C22⋊C4C23×D1116yes—
884C42—111no—
885C42—111no—
886C42—111no—
887C42—113no—
888C42—113no—
889C42—113no—
890C42—113no—
891C42—113no—
892C42—113no—
893C42—113no—
894C42—113no—
895C42—113no—
896C42—1112no—
897C42—1112no—
898C42—1112no—
899C42C23×D1111yescharacteristic
900C42C23×D1113yes—
901C42C23×D1113yes—
902C42C23×D1113yes—
903C42C23×D11112yes—
904C11C2×#350311yescharacteristic, complemented, Sylow
905C23—111no—
906C23—1112no—
907C23—113no—
908C23—226no—
909C23—226no—
910C23C24×D1113yes—
911Q8—212no—
912Q8—24no—
913Q8—412no—
914Q8—1112no—
915Q8—2224no—
916Q8—228no—
917Q8—2212no—
918Q8—224no—
919Q8—4412no—
920Q8—4424no—
921Q8C2×Q8×D1114yescomplemented
922D4—1124no—
923D4—1112no—
924D4C2×Q8×D11112yescomplemented
925C2×C4—26no—
926C2×C4—26no—
927C2×C4—412no—
928C2×C4—1112no—
929C2×C4—113no—
930C2×C4—111no—
931C2×C4—111no—
932C2×C4—111no—
933C2×C4—114no—
934C2×C4—1112no—
935C2×C4—1112no—
936C2×C4—1112no—
937C2×C4—114no—
938C2×C4—114no—
939C2×C4—114no—
940C2×C4—113no—
941C2×C4—113no—
942C2×C4—1112no—
943C2×C4—226no—
944C2×C4—226no—
945C2×C4—226no—
946C2×C4—226no—
947C2×C4—2224no—
948C2×C4—228no—
949C2×C4—226no—
950C2×C4—226no—
951C2×C4—226no—
952C2×C4—226no—
953C2×C4—4424no—
954C2×C4—4412no—
955C2×C4C2×Q8×D11112yescomplemented
956C2×C4C24×D1114yes—
957C2×C4C24×D1113yes—
958C2×C4C24×D1113yes—
959C2×C4C24×D11112yes—
960C2×C4C24×D1113yes—
961C2×C4C24×D1111yescharacteristic
962C2×C4C24×D1111yescharacteristic
963C2×C4C24×D1111yescharacteristic
964C22—23no—
965C22—23no—
966C22—112no—
967C22—112no—
968C22—112no—
969C22—116no—
970C22—2224no—
971C22—223no—
972C22—223no—
973C22C22×Q8×D1116yes—
974C22C25×D1111yescharacteristic
975C4—23no—
976C4—212no—
977C4—23no—
978C4—24no—
979C4—112no—
980C4—116no—
981C4—112no—
982C4—112no—
983C4—223no—
984C4—2212no—
985C4—223no—
986C4—224no—
987C4C22×Q8×D1112yes—
988C4C22×Q8×D1116yes—
989C4D11×H(5,𝔽2)12yes—
990C4D11×2−1+412yes—
991C2—26no—
992C2—114no—
993C2—226no—
994C2C23×Q8×D1111yescharacteristic
995C2C2×D11×H(5,𝔽2)11yescharacteristic
996C2C2×D11×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C25×D11
commutator, socle, cosocleC22×C11C26
FittingC11×#3503C2
prime radicalC2×#41×D11C22
hypercenter#3503D11
hypocenterC11C2×#3503
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #3503

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13082435C2semidirect
2. #13082434C2semidirect
3. #13082433C2semidirect
4. #13082432C2semidirect
5. #13082431C2semidirect
6. #13082430C2semidirect
7. #13082429C2semidirect
8. #13082428C2semidirect
9. #13082427C2semidirect
10. Q82×D11C2semidirect
11. D11×#557C2semidirect
12. D11×#554C2semidirect
13. D4×Q8×D11C2semidirect
14. D11×#544C2semidirect
15. D11×#533C2semidirect
16. C2×D11×C4⋊Q8C2semidirect
19. C11×#3503C2semidirect
22. Q82×C11C22semidirect
23. C11×#557C22semidirect
24. C11×#554C22semidirect
25. D4×Q8×C11C22semidirect
26. C11×#544C22semidirect
27. C11×#533C22semidirect
28. C2×C11×C4⋊Q8C22semidirect
33. Q8×C22⋊D11C22semidirect
34. C2×#66997C22semidirect
35. #10623261C22semidirect
36. #10623260C22semidirect
37. #10623260C22semidirect
38. #10623259C22semidirect
39. #10623259C22semidirect
40. #10623258C22semidirect
41. #10623258C22semidirect
48. D11×C4⋊Q8C22semidirect
49. D11×C4⋊Q8C22semidirect
50. D11×C4⋊Q8C22semidirect
51. D11×C4⋊Q8C22semidirect
52. #10623253C22semidirect
53. #10623253C22semidirect
54. #10623252C22semidirect
55. #10623221C22semidirect
56. #10623220C22semidirect
57. #10623220C22semidirect
58. #10623219C22semidirect
61. #10623216C22semidirect
62. #10623167C22semidirect
63. #10623166C22semidirect
64. #10623163C22semidirect
65. #10623163C22semidirect
69. #10623154C22semidirect
70. #10623153C22semidirect
71. #10623153C22semidirect
72. #10623110C22semidirect
73. #10623109C22semidirect
74. #10623109C22semidirect
75. Q8×D44C22semidirect
84. #10623101C22semidirect
85. #10623100C22semidirect
86. #10623098C22semidirect
87. Q8×Dic22C22semidirect
88. Q8×Dic22C22semidirect
89. Q8×Dic22C22semidirect
94. #10623074C22semidirect
95. #10623070C22semidirect
96. D4×Dic22C22semidirect
97. D4×Dic22C22semidirect
104. #10623050C22semidirect
105. #10623050C22semidirect
106. #10623048C22semidirect
107. #10623042C22semidirect
111. #10623031C22semidirect
112. C2×#66941C22semidirect
113. C2×#66941C22semidirect
116. #10623001C22semidirect
117. C2×#66922C22semidirect
120. #41×D11Q8semidirect
292. C11×#41C2×Q8semidirect
308. #4343C2×Q8semidirect
314. Q8×D11C2×Q8semidirect
315. #4341C2×Q8semidirect
316. D4×D11C2×Q8semidirect
317. #4339C2×Q8semidirect
322. C2×C4×D11C2×Q8semidirect
416. #3503D11direct (N × H)
435. Q8×C11C22×Q8semidirect
436. D4×C11C22×Q8semidirect
440. C2×C4×C11C22×Q8semidirect
449. C22⋊D11C22×Q8semidirect
453. C2×Dic11C22×Q8semidirect
462. D44C22×Q8semidirect
474. C4×D11C22×Q8semidirect
475. C4×D11C22×Q8semidirect
484. Dic22C22×Q8semidirect
492. Q82C2×D11semidirect
498. #557C2×D11semidirect
507. #554C2×D11semidirect
516. D4×Q8C2×D11semidirect
525. #544C2×D11semidirect
535. #533C2×D11semidirect
550. C2×C4⋊Q8C2×D11semidirect
787. D11#3503direct (N × H)
792. #41Q8×D11semidirect
904. C11C2×#3503semidirect
921. Q8C2×Q8×D11semidirect
924. D4C2×Q8×D11semidirect
955. C2×C4C2×Q8×D11semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130824352
#130824342
#130824332
#130824322
#130824312
#130824302
#130824292
#130824282
#130824272
Q82×D112
D11×#5572
D11×#5542
D4×Q8×D112
D11×#5442
D11×#5332
C2×D11×C4⋊Q82
D11×#5202
C4×#41×D112
C11×#35032
C2×#350311